As the Internet of Things technology develops rapidly, cyber-physical systems (CPSs) have provided critical technologies in the industrial field. A smart grid is a typical application of the CPS, which is formed by the coupling of the power network and communication network. In general, the two networks are heterogeneous. Considering the characteristics of the power network, the ordinary percolation network model is not suitable for the network carrying physical flow. Therefore, we propose an interdependent network model with a load. That is, nodes in the physical network have loaded. Then, we research the security of CPS under the multi-load mode. The rule for node failure is different from the percolation model. When a node’s load exceeds its capacity, the node fails. Through the theoretical analysis, we obtained the iterative equation of the percolation threshold and analyzed it through simulation experiments. We adopt both linear and nonlinear capacity models. It is found that appropriately increasing the average degree of ER network can improve its ability to resist attacks. In contrast, the power exponent of the SF network has less influence on the critical value of network percolation. In addition, we found that increasing the capacity parameter in the linear capacity model can improve the robustness of the network, where the variation of the ER-ER network is more evident than that of the SF-SF network. Increasing the capacity parameter in the nonlinear capacity model can significantly increase the network’s ability to resist attacks. However, due to the increase in economical cost, we can improve the network’s reliability by increasing the node capacity while controlling the cost.